Finite Group Databasebeta

← C2×C7×#13109900 #37524508

Subgroups — C2×C7×#13109900 #37524508

Order 22932.

128 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#11717941C211yesmaximal, characteristic, complemented
2C7×#13109900C211yesmaximal, characteristic, direct product factor
3C7×#13109900C211yesmaximal, characteristic, direct product factor
4C2×C3×C7×C13×D7C311yesmaximal, characteristic
5C7×#11717941C2211yescharacteristic, complemented, Hall
6C3×C7×C13×D7C2×C311yescharacteristic
7C3×C7×C13×D7C2×C311yescharacteristic
8C2×C3×C72×C13C2×C311yescharacteristic
9C22×C7×C13⋊C9—71nomaximal
10C2×#13109900C711yesmaximal, characteristic, direct product factor
11C2×C7×C13×D7C911yescharacteristic, complemented, Hall
12C3×C72×C13C22×C311yescharacteristic
13C2×C7×D7⋊C9—131nomaximal, Hall
14C2×#11717941C2×C711yescharacteristic, complemented
15C2×C7×C13⋊C9—71no—
16C2×C7×C13⋊C9—71no—
17C2×C7×C13⋊C9—71no—
18#13109900C2×C711yescharacteristic, direct product factor
19#13109900C2×C711yescharacteristic, direct product factor
20C2×C72×C13C2×C911yescharacteristic, complemented
21C7×C13×D7C2×C911yescharacteristic, complemented
22C7×C13×D7C2×C911yescharacteristic, complemented
23C22×C3×C7×C13—211no—
24C2×C3×C13×D7C3×C711yescharacteristic
25C2×C7×C7⋊C9—131no—
26C7×D7⋊C9—131no—
27C7×D7⋊C9—131no—
28#11717941C22×C711yescharacteristic, complemented
29C7×C13⋊C9—71no—
30C72×C13C22×C911yescharacteristic, complemented, Hall
31C2×C3×C7×D7C13⋊C311yescharacteristic
32C2×C3×C7×C13—61no—
33C2×C3×C7×C13—211no—
34C2×C3×C7×C13—211no—
35C2×C3×C7×C13AGL(1,𝔽7)11yescharacteristic
36C2×C3×C7×C13C2×C3×C711yescharacteristic
37C3×C13×D7C2×C3×C711yescharacteristic
38C3×C13×D7C2×C3×C711yescharacteristic
39C22×C13⋊C9—71noHall
40C7×C7⋊C9—131noHall
41C22×C7×C13—211no—
42C2×C13×D7C7×C911yescharacteristic, complemented
43C2×C3×C72C2×C13⋊C311yescharacteristic
44C3×C7×D7C2×C13⋊C311yescharacteristic
45C3×C7×D7C2×C13⋊C311yescharacteristic
46C3×C7×C13—61no—
47C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
48C3×C7×C13C22×C3×C711yescharacteristic
49C22×C7×C9—911no—
50C2×D7⋊C9—131no—
51C2×C13⋊C9—71no—
52C2×C13⋊C9—71no—
53C2×C13⋊C9—71no—
54C2×C7×D7C13⋊C911yescharacteristic, complemented, Hall
55C2×C7×C13—61no—
56C2×C7×C13—211no—
57C2×C7×C13—211no—
58C2×C7×C13D7⋊C911yescharacteristic, complemented
59C2×C7×C13C2×C7×C911yescharacteristic, complemented
60C13×D7C2×C7×C911yescharacteristic, complemented
61C13×D7C2×C7×C911yescharacteristic, complemented
62C22×C3×C13—71no—
63C3×C72C22×C13⋊C311yescharacteristic
64C2×C7×C9—911no—
65C2×C7×C9—911no—
66C2×C7×C9—911no—
67C2×C7⋊C9—131no—
68D7⋊C9—131no—
69D7⋊C9—131no—
70C13⋊C9—71noHall
71C2×C72C2×C13⋊C911yescharacteristic, complemented
72C7×D7C2×C13⋊C911yescharacteristic, complemented
73C7×D7C2×C13⋊C911yescharacteristic, complemented
74C7×C13—61no—
75C7×C13C2×D7⋊C911yescharacteristic, complemented
76C7×C13C22×C7×C911yescharacteristic, complemented
77C22×C3×C7—71no—
78C2×C3×D7C7×C13⋊C311yescharacteristic
79C2×C3×C13—211no—
80C2×C3×C13—211no—
81C2×C3×C13C7×AGL(1,𝔽7)11yescharacteristic
82C7×C9—911no—
83C7⋊C9—131no—
84C22×C13—71noHall
85C72C22×C13⋊C911yescharacteristic, complemented, Sylow
86C2×C3×C7—61no—
87C2×C3×C7—71no—
88C2×C3×C7—211no—
89C2×C3×C7#1058772011yescharacteristic
90C2×C3×C7C2×C7×C13⋊C311yescharacteristic
91C3×D7C2×C7×C13⋊C311yescharacteristic
92C3×D7C2×C7×C13⋊C311yescharacteristic
93C3×C13C2×C7×AGL(1,𝔽7)11yescharacteristic
94C22×C9—911noHall
95C22×C7—71no—
96C2×D7C7×C13⋊C911yescharacteristic, complemented
97C2×C13—211no—
98C2×C13—211no—
99C2×C13C7×D7⋊C911yescharacteristic, complemented
100C3×C7—61no—
101C3×C7C2×#1058772011yescharacteristic
102C3×C7C22×C7×C13⋊C311yescharacteristic
103C2×C9—911no—
104C2×C9—911no—
105C2×C9—911no—
106C2×C7—61no—
107C2×C7—71no—
108C2×C7—211no—
109C2×C7#1310990011yescharacteristic, direct product factor
110C2×C7C2×C7×C13⋊C911yescharacteristic, complemented
111D7C2×C7×C13⋊C911yescharacteristic, complemented
112D7C2×C7×C13⋊C911yescharacteristic, complemented
113C13C2×C7×D7⋊C911yescharacteristic, complemented, Sylow
114C22×C3—211no—
115C9—911noSylow
116C7—61no—
117C7C2×#1310990011yescharacteristic, direct product factor
118C7C22×C7×C13⋊C911yescharacteristic, complemented
119C2×C3—211no—
120C2×C3—211no—
121C2×C3C7×#1058772011yescharacteristic
122C22—211noSylow
123C3C2×C7×#1058772011yescharacteristic
124C2—211no—
125C2—211no—
126C2C7×#1310990011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7#10587720
commutator, hypocenterC7×C13C22×C7×C9
FrattiniC3C2×C7×#10587720
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C7×C13×D7C3
cosocleC3×C7×C13C22×C3×C7
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#11717941C2semidirect
2. C7×#13109900C2direct (N × H)
3. C7×#13109900C2direct (N × H)
5. C7×#11717941C22semidirect
10. C2×#13109900C7direct (N × H)
11. C2×C7×C13×D7C9semidirect
14. C2×#11717941C2×C7semidirect
18. #13109900C2×C7direct (N × H)
19. #13109900C2×C7direct (N × H)
20. C2×C72×C13C2×C9semidirect
21. C7×C13×D7C2×C9semidirect
22. C7×C13×D7C2×C9semidirect
28. #11717941C22×C7semidirect
30. C72×C13C22×C9semidirect
42. C2×C13×D7C7×C9semidirect
54. C2×C7×D7C13⋊C9semidirect
58. C2×C7×C13D7⋊C9semidirect
59. C2×C7×C13C2×C7×C9semidirect
60. C13×D7C2×C7×C9semidirect
61. C13×D7C2×C7×C9semidirect
71. C2×C72C2×C13⋊C9semidirect
72. C7×D7C2×C13⋊C9semidirect
73. C7×D7C2×C13⋊C9semidirect
75. C7×C13C2×D7⋊C9semidirect
76. C7×C13C22×C7×C9semidirect
85. C72C22×C13⋊C9semidirect
96. C2×D7C7×C13⋊C9semidirect
99. C2×C13C7×D7⋊C9semidirect
109. C2×C7#13109900direct (N × H)
110. C2×C7C2×C7×C13⋊C9semidirect
111. D7C2×C7×C13⋊C9semidirect
112. D7C2×C7×C13⋊C9semidirect
113. C13C2×C7×D7⋊C9semidirect
117. C7C2×#13109900direct (N × H)
118. C7C22×C7×C13⋊C9semidirect
126. C2C7×#13109900direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#117179412
C7×#131099002
C2×C3×C7×C13×D73
C22×C7×C13⋊C97
C2×#131099007
C2×C7×D7⋊C913